Try using Soundflower.
First make sure your volume is up. Then set Soundflower (2ch) as your default system audio output device (opt+click the volume icon and select it), launch Soundflowerbed (from /Applications/Soundflower/) and click the new flower icon in your menubar, and select your normal output from the Soundflower (2ch) heading there (headphones, in this case). Then go into OBS's Audio settings and set it to use Soundflower (2ch) as your Desktop Audio device.